Sen. Minority Leader Mitch McConnell, R-Ky., urged Majority Leader Harry Reid, D-Nev., to allow amendments to a Ukrainian aid package in order to secure its passage through the House.

“Look: this bill cannot pass the House or become law in its current form—it must be amended,” McConnell said on the Senate floor.

Some Senate Republicans object to a provision in the Senate bill that would approve an overhaul of the structure of the International Monetary Fund, which they argue would end up costing taxpayers. The Republican-run House left the provision out of Ukraine aid bills they have drafted despite a request from the White House that it be included.

McConnell wants Reid to allow amendments to the measure in order to address the issue.

But Democrats may not be inclined to offer amendments to Republicans given that they appear to have the 60 votes needed to pass the bill. The measure cleared a procedural vote 78 to 17 Monday evening.

“In order for it to become law, the controversial IMF provision must be removed,” McConnell continued. “This simply cannot be a take-or-leave-it situation. That’s just nonsensical.”

“That means allowing a sensible amendment process,” McConnell said. “And it means dropping the kind of wild partisan accusations we’ve seen – attacks that will only make it that much harder to get to an effective, bipartisan solution.”

A bipartisan House bill would strip the IMF provisions from the Senate bill. But Reid has been attacking Republicans over a push they made earlier this month to allow the IMF language in exchange for including a provision blocking the Internal Revenue Service from imposing new restrictions on the political activities of groups such as Americans for Prosperity, which is backed by the Koch brothers.

Reid and Democratic leaders have said that they want to hold more amendment votes this year and could be amenable to some votes. But Democrats don't want delays in passing the bill, either.

Senate Majority Whip Richard J. Durbin, D-Ill., on the Senate floor Monday invited those with amendments make them known to leaders.

"If the other side or any senator has a proposal for an amendment I hope they won't keep it to themselves,” he said. “Let's talk about it, let's see if we can amend this measure, change this measure in a constructive fashion without introducing a lot of amendments that might bog us down in long-term debate. The Ukrainians are waiting to hear from the United States.”

Possible amendments to the bill include a proposal from Sen. Ted Cruz, R-Texas, that would strike the IMF provision, and a plan from Sen. John Barrasso, R-Wyo., who wants to offer a proposal expediting liquid natural gas exports.

Durbin urged caution on new gas exports.

"It is a newfound treasure and its one that we ought to be careful and measure carefully. Some say we have plenty...others say take care, make certain that we make the decision that is best for America," Durbin said. "Should we debate that and decide that in a matter of minutes or hours on the floor of the Senate this week of take the time to look at it carefully? I think the latter."